How the Ofsted chief got his maths wrong on Sats

Sir Michael Wilshaw last night condemned the failure of some children to achieve the national average in English Sats aged 11. Today his office admits that was a "slip of the tongue" – the average is a mathematical calculation rather than a "target". But what does his error tell us about the Sats system? Polly Curtis, with your help, finds out. Get in touch below the line, Tweet @pollycurtis or email polly.curtis@guardian.co.uk.

The head of Ofsted, Sir Michael Wilshaw, said it was long recognised that 'satisfactory' was not good enough. Photograph: Felix Clay

Last night on Newsnight Sir Michael Wilshaw, the chief inspector of schools and head of Ofsted, condemned the fact that one in five pupils are leaving primary school without reaching the "national average" in English. His comment led to accusations on Twitter that he had been "statistically incoherent", including this one from @Bickerrecord:

Our standards should be higher. What that in effect means is something like one in five children in primary schools at the age of 11 are leaving primary school without the national average. What that really means is that they can't access the curriculum in secondary school, they find it difficult to pass examinations, they find it difficult to proceed to the next stage of their education and training, and of course they find it difficult to get jobs.

It is of course unsurprising that some children weren't average: some children will inevitably be below average, because an average is just a measure of the most typical outcome for children. It is statistically incoherent to condemn a system for some children failing to reach the national average. To repeat, some children will always fail to reach the average.

The chief inspector's comments are based on this Ofsted report, which makes it clear that what he is actually referring to is the "national expectation" or target. It says:

Standards in English at the end of Key Stage 2 have also not risen since the last report. While four-fifths of pupils at Key Stage 2 reached national expectations over the last three years, one in five primary pupils did not achieve the expected standard in English.

On the phone just now, the Ofsted press office admitted that Wilshaw's reference to the average was simply a "slip of the tongue" and the language in the report is correct.

But it's quite a telling one. There has always been a blurring between averages and targets. The current target for primaries is that 85% of children should make two levels of progress between years two and six in English. Last year 82% got a level four in English and 29% got a level five.

What happened is that in 1988 when they were thinking about introducing the Sats there was a graph in the report that created the level system which found that the middle of level four is the median. It's a mathematical expectation – that's what we expect a child to get. Politicians adopted that as a target and that moved to a minimum expectation. It's not impossible to think that something that was originally set as an average, should become a minimum. If 80% are hitting it, then the average performance is higher than the threshold of the level. By moving the target above average it's saying we can't accept what used to be average as good now because of the improvements in the results.

Average expected levels 1987. Source: Task Group on Assessment and Testing

Sir Michael is recommending that the bar needs to be raised from demanding that ever larger numbers of children achieve the average or expected level 4 to raising that standard entirely. Within each level there are three categories A, B and C. He's arguing that schools should be expected to get children towards the top level A, rather than C, because there is a lot of evidence that that level four As correlate with good GCSEs, and level four Cs don't. Reality check looked at this previously here. Today Sir Michael said:

Last year 45% of those pupils who just reached level 4C at the age of 11 did not achieve a grade C in their GCSE English exams. So one of the first questions we need to ask is whether the national end-of-primary-school target of level 4 is sufficiently high to provide an adequate foundation for success at secondary school.

Our education editor Jeevan Vasagar has just pointed me towards this exchange in the Commons education select committee, this time exposing the education secretary Michael Gove's problems with understanding averages.

Chair: Secretary of State, we are moving to a novel, new section: quick fire questions and answers, inspired by the Twitter feed #askgove-5,000-plus wanting to interact with you. So we are going to go round each of us in fairly strict timing. If you could give us quick answers, that would be great.

Michael Gove: I will try my best.

Chair: One is: if "good" requires pupil performance to exceed the national average, and if all schools must be good, how is this mathematically possible?